Rationality in four dimensions

By leveraging the physics of the Higgs branch, we argue that the conformal central charges a and c of an arbitrary 4D N=2 superconformal field theory (SCFT) are rational numbers. Our proof of the rationality of c is conditioned on a well-supported conjecture about how the Higgs branch of an SCFT is encoded in its protected chiral algebra. To establish the rationality of a, we further rely on a widely believed technical assumption on the high-temperature limit of the superconformal index.